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Table 9.

Eigenvectors of the characteristic equation for each of the three locusts

Eigenvectors
LocustModeδu/uePhase angle (degrees)δw/ue ≈δαbPhase angle (degrees)δq (rad s−1)Phase angle (degrees)δθ (rad)Phase angle (degrees)
`R' Oscillatory 0.044 −90.4 1.0 −2.9 62 −94.5 
 Divergence −0.26  0.64  5.0   
 Subsidence 2.8  −7.0  −2.5   
`G' Oscillatory 0.090 91.4 1.0 3.6 101 94.1 
 Divergence −0.52  0.46  5.7   
 Subsidence 1.3  −1.1  −3.5   
`B' Oscillatory 0.038 89.8 1.0 3.7 56 95.4 
 Divergence −0.19  0.62  6.0   
 Subsidence −4.9  16.6  −3.9   
Eigenvectors
LocustModeδu/uePhase angle (degrees)δw/ue ≈δαbPhase angle (degrees)δq (rad s−1)Phase angle (degrees)δθ (rad)Phase angle (degrees)
`R' Oscillatory 0.044 −90.4 1.0 −2.9 62 −94.5 
 Divergence −0.26  0.64  5.0   
 Subsidence 2.8  −7.0  −2.5   
`G' Oscillatory 0.090 91.4 1.0 3.6 101 94.1 
 Divergence −0.52  0.46  5.7   
 Subsidence 1.3  −1.1  −3.5   
`B' Oscillatory 0.038 89.8 1.0 3.7 56 95.4 
 Divergence −0.19  0.62  6.0   
 Subsidence −4.9  16.6  −3.9   

Each row of eigenvectors corresponds to one of the roots, or eigenvalues,in Table 7 and gives the relative magnitudes and phases of the state variables that satisfy the corresponding solution to the characteristic equation.

The values of the eigenvectors are arbitrary to within a complex factor,and the eigenvectors are therefore normalised to give the pitch attitude disturbance δθ a magnitude of 1 rad and phase angle of zero.

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